Cultist A scores a success on the damage roll, making the Professor shaken. Cultist B then scores a raise on the damage roll, causing the Professor a wound. Professor takes one wound in total, and is shaken.

or

Cultist B scores a raise on the damage roll, causing the Professor a wound and making him shaken. Cultist A then scores a success on the damage roll, (a "shaken" result). A damaging attack's result of "shaken" when the victim is already shaken results in a wound. Professor takes two wounds in total, and is shaken."

Is this one of those "order does matter" cases, or have I gotten something wrong?

If the cultists go on the same initiative, does the person controlling them choose which cultist goes first?

Cultist A scores a success on the damage roll, making the Professor shaken. Cultist B then scores a raise on the damage roll, causing the Professor a wound. Professor takes one wound in total, and is shaken.

or

Cultist B scores a raise on the damage roll, causing the Professor a wound and making him shaken. Cultist A then scores a success on the damage roll, (a "shaken" result). A damaging attack's result of "shaken" when the victim is already shaken results in a wound. Professor takes two wounds in total, and is shaken."

Is this one of those "order does matter" cases, or have I gotten something wrong?

If the cultists go on the same initiative, does the person controlling them choose which cultist goes first?

Yep, order does matter, and if they all act on the same initiative card, the person controlling them decides how to apply them.

So really, unless they go on different initiative cards, the first one isn't going to happen._________________Clint Black
Savage Worlds Core Rules Brand Manager